At the heart of the axion solution to the strong CP problem lies the fact that the QCD anomaly is the only source of explicit PQ breaking. As a byproduct, within the so-called canonical axions the \(m_a\) -\(f_a\)  relation is fixed by QCD [1]}, [2]},

maQCD f mfa mu mdmu+md ,


where \(m_\pi , f_\pi , m_u\)  and \(m_d\)  denote respectively the pion mass, its decay constant, and the up and down quark masses. The strength of the axion couplings to Standard Model (SM) fields is instead model-dependent: it varies with the matter content of the UV complete axion model.
